Number of Baxter permutations: A001181/2.

Terms

a(0) =1a(1) =3a(2) =11a(3) =46a(4) =211a(5) =1037a(6) =5377a(7) =29101a(8) =163120a(9) =941480a(10) =5570280a(11) =33664996a(12) =207249719a(13) =1296670793a(14) =8229378293a(15) =52895993341a(16) =343891293422